Inference by replication in densely connected systems

TL;DR

This paper introduces an advanced Bayesian inference method using replicated message passing for dense systems, extending replica symmetry assumptions to improve performance in complex noise environments like CDMA.

Contribution

It extends the replica symmetric approach to include one-step replica symmetry breaking, enhancing inference accuracy in complex, noisy dense systems.

Findings

Efficient signal detection algorithm for CDMA under non-critical regimes

Identification of a first order transition line in the critical regime

Performance improvement using 1RSB ansatz in complex noise models

Abstract

An efficient Bayesian inference method for problems that can be mapped onto dense graphs is presented. The approach is based on message passing where messages are averaged over a large number of replicated variable systems exposed to the same evidential nodes. An assumption about the symmetry of the solutions is required for carrying out the averages; here we extend the previous derivation based on a replica symmetric (RS) like structure to include a more complex one-step replica symmetry breaking (1RSB)-like ansatz. To demonstrate the potential of the approach it is employed for studying critical properties of the Ising linear perceptron and for multiuser detection in Code Division Multiple Access (CDMA) under different noise models. Results obtained under the RS assumption in the non-critical regime give rise to a highly efficient signal detection algorithm in the context of CDMA; while in the critical regime one observes a first order transition line that ends in a continuous phase transition point. Finite size effects are also observed. While the 1RSB ansatz is not required for the original problems, it was applied to the CDMA signal detection problem with a more complex noise model that exhibits RSB behaviour, resulting in an improvement in performance.